Blender 2.82 subdivision problem
If you're talking about the mesh visibility, it's normal you can't see some vertices as you've given your object a Subdivision Surface modifier. This modifier slightly deforms your surface, but the vertices are still displayed at their original position, so they might be hidden by the surface deformations. If you want the vertices to stick to the position that they will have once the modifier is applied, enable the modifier's On Cage option:

The other problem you're probably talking about is the fact that your vertices stick to the surface as soon as you're moving them, and that's because you've enabled the Snapping option: